Question 1:

The acceleration of a body is the rate of change of velocity.

Acceleration is a vector quantity, meaning it has both magnitude and direction. It describes how the velocity of an object changes over time. This change can be an increase in speed, a decrease in speed (deceleration), or a change in direction.

• Rate of change of speed (B): Speed is a scalar quantity (magnitude only). A change in direction at a constant speed, such as in uniform circular motion, is an acceleration, but it wouldn't be captured by the rate of change of speed alone.

• Rate of change of position (C): The rate of change of position is velocity.

• Rate of change of displacement (D): The rate of change of displacement is also velocity. Displacement is a vector quantity that describes the change in an object's position.

  The correct answer is A.

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Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 2:

Velocity vs. Speed

It's a common misconception to use "velocity" and "speed" interchangeably, but in physics, they're distinct concepts.

• Velocity is a vector quantity, meaning it has both magnitude (how fast you're going) and direction (where you're going). For example, "10 meters per second, due east" is a velocity.

• Speed is a scalar quantity, meaning it only has magnitude. For example, "10 meters per second" is a speed. A car's speedometer measures its instantaneous speed, not its velocity, because it doesn't show the direction.

A change in direction, even at a constant speed, means a change in velocity and therefore an acceleration. For instance, a car driving around a circular track at a constant 60 mph has a constant speed but a constantly changing velocity because its direction is always changing.

The correct answer is C. The velocity of a body is the rate of change of position.

Why the other options are incorrect:

• A. rate of change of acceleration: This is called jerk, which describes how quickly an object's acceleration changes.

• B. rate of change of speed: This isn't a standard term in physics because it ignores direction. While a change in speed does indicate a change in velocity, this option is incomplete because velocity also changes with a change in direction.

• D. rate of change of motion: This is a vague term not used in a precise, scientific context. "Motion" can refer to many things, while "position," "velocity," and "acceleration" are all specific, measurable quantities.

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 3:

The correct answer is B. displacement, velocity, acceleration.

These are all vector quantities, meaning they have both magnitude (a size or numerical value) and direction.

Vectors vs. Scalars

• Vectors are quantities that have both magnitude and direction. Think of a car traveling at "60 mph to the north." This is a vector because it includes both speed and a specific direction.

• Scalars are quantities that have only magnitude. Think of a car traveling at "60 mph." This is a scalar because it only tells you how fast the car is going, not where it's headed.

Analyzing the Options

Let's break down each quantity listed in the options:

• Displacement: This is the change in an object's position. It's a vector because it's the straight-line distance from the starting point to the ending point, including a specific direction. For example, "5 meters east."

• Distance: This is the total length of the path traveled. It's a scalar because it doesn't care about the direction of travel. For example, if you walk 5 meters east and then 5 meters west, your total distance traveled is 10 meters, but your displacement is 0 meters.

• Velocity: This is the rate of change of displacement. It's a vector because it includes both speed and direction. A change in direction, even at a constant speed, means the velocity is changing.

• Speed: This is the rate of change of distance. It's a scalar because it only measures how fast something is moving, without regard to its direction.

• Acceleration: This is the rate of change of velocity. It's a vector because it describes a change in velocity, which can be a change in speed, a change in direction, or both.

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 4:

Calculating Average Acceleration

Average acceleration is the change in velocity over a specific time interval. The formula is:

• a avg​ is the average acceleration.

• v_f is the final velocity.

• v_i is the initial velocity.

• t_f is the final time.

• t _i is the initial time.

Applying the Formula to the Graph

From the graph provided:

• Initial Velocity ( v_i): At time t = 0 s, the velocity is 0 m/s.

• Final Velocity ( v_f): At time t = 10 s, the velocity is 20 m/s.

• Time Interval ( Δt): The change in time is 10 s - 0 s = 10 s.

Now, plug these values into the formula:

Therefore, the average acceleration of the ball over the first 10 seconds is 2 ms^-2.

The correct answer is B. 2 ms^-2.

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 5: (edited by the Silverback)

*Instantaneous Acceleration at t = 0 s and t = 10 s

Instantaneous acceleration is the slope of the velocity-time graph at a specific point in time. Since the graph shown is not straight line, the acceleration changes.

• Slope Calculation:

  Slope = Δv/Δt ​ = 10 /1 for the first 1 second shown, = 10 ms^-2

Because the acceleration is approximately constant over the first second, the instantaneous acceleration at any point is the same as the average acceleration over that time interval. Therefore, the instantaneous acceleration is:

• at t = 0 s: 10 ms^-2

• at t = 10 s, the line is horizontal, so the gradient =0, and the acceleration = 0 ms^-2.

Based on this analysis, option C is correct.

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 6:

Velocity and Acceleration during the First 5 Seconds

• Velocity: The velocity starts at 0 m/s and increases to 20 m/s during the first 5 seconds. Since the velocity is changing (not constant), it is described as non-uniform.

• Acceleration: The acceleration is the slope or gradient of the velocity-time graph. Since the graph changes gradient during the first 5 seconds, the gradient is not constant. This means the acceleration is also non-uniform.

Therefore, the velocity is non-uniform, and the acceleration is also non-uniform. This corresponds to option D.

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 7:

The Parabolic Path of a Projectile

The path of a projectile, known as its trajectory, is a parabola when air resistance is ignored. This is due to two independent components of motion:

• Horizontal motion: The projectile moves at a constant velocity because there are no horizontal forces acting on it.

• Vertical motion: The projectile is constantly accelerating downwards due to the force of gravity.

The combination of these two motions—constant horizontal velocity and constant vertical acceleration—results in a parabolic curve.

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 8:

Calculating the Vertical Component of Initial Velocity

The initial velocity of the projectile is a vector with both a horizontal and a vertical component. We can resolve this vector using trigonometry.

• The initial velocity magnitude is v = 10 ms ⁻¹.

• The launch angle is θ = 30°.

• The vertical component ( v_y ) is opposite to the angle θ in the right-angled triangle formed by the velocity vectors.

• The horizontal component ( v_x) is adjacent to the angle θ.

Using the sine function, which relates the opposite side to the hypotenuse:

Rearranging the formula to solve for the vertical component (v_y):

Plugging in the given values:

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 9:

The incorrect statement is C. The time taken to reach the impact point stays the same.

Here's why:

• A. The maximum height reached increases. This is correct. Maximum height ( h max​) depends on the initial vertical velocity component, v_y​ . The formula is h max​ = 2.g.v_y ^2​ ​ .
  Since increasing the initial velocity ( v) without changing the launch angle increases the vertical component ( v_y​​ = v sin θ), the maximum height reached will increase.

• B. The total distance travelled increases. This is also correct. The total horizontal distance, or range ( R), is given by R = g v ² sin(2θ)​ . Since v is in the numerator, increasing the initial velocity will increase the total distance traveled.

• C. The time taken to reach the impact point stays the same. This is incorrect. The time of flight ( T) depends on the initial vertical velocity component,v_y​​ . The formula is T = g 2v_y​​ ​ ​ = g 2v sin θ​ . Increasing the initial velocity ( v) will increase the vertical component (v_y​​ ), which in turn increases the total time the projectile stays in the air.

• D. The impact velocity also increases. This is correct. In the absence of air resistance, the projectile's impact speed is equal to its initial speed. Since the initial velocity is increased, the impact velocity will also be greater. While the direction may be different (downward), the magnitude of the velocity upon impact is the same as the magnitude of the initial velocity.

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.

Question 10:

When a projectile is affected by air resistance, its path is altered from the ideal parabolic curve. Air resistance is a force that opposes the direction of motion, acting on both the horizontal and vertical components of the projectile's velocity.

How Air Resistance Affects Projectile Motion

• Horizontal Motion: Air resistance acts as a constant braking force, reducing the projectile's horizontal velocity. This causes the projectile to travel a shorter horizontal distance (range) than it would in a vacuum.

• Vertical Motion:

  • On the way up: The projectile is moving upwards, so air resistance acts downwards, in the same direction as gravity. This increases the total downward force, causing the projectile to reach its maximum height faster and at a lower altitude than in the ideal case.

  • On the way down: The projectile is moving downwards, so air resistance acts upwards, opposing the force of gravity. This reduces the net downward force and acceleration, causing the projectile to fall back to the ground more slowly.

Comparing the solid curves to the ideal, dotted-line path:

• Curves A and B show a greater maximum height, which is incorrect. Air resistance always reduces the maximum height.

• Curve D shows a shorter maximum height but a longer range, which is also incorrect. Air resistance reduces the horizontal distance traveled.

• Curve C correctly shows a lower maximum height and a shorter horizontal range, which are the combined effects of air resistance acting on the projectile's motion. The path is also no longer a perfect parabola; it is asymmetric, with a steeper upward trajectory and a shallower downward one.

Edit: Good attempt and explanations A.I. bot but you have not read the diagrams correctly. The reduced maximum height and horizontal distance is curve A.

The Silverback

*These A.I. responses may be incorrect. Responses may give guidance but the A.I. might not be able to answer the question! This is particularly the case for questions based on diagrams, which the A.I. typically cannot interpret.
Grade Gorilla uses Gemini, Deepseek and a range of other A.I. chatbots to generate the saved responses. Some answers have had human intervention for clarity or where the A.I. has not been able to answer the question.